@@ Property / Symbols used @@
+Ferrers function of the first kind
@@ Property / Symbols used: Ferrers function of the first kind / rank @@
+Normal rank
@@ Property / Symbols used: Ferrers function of the first kind / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}$ 
\FerrersP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
@@ Property / Symbols used: Ferrers function of the first kind / qualifier @@
+xml-id: C14.S3.E1.m2aadec
@@ Property / Symbols used @@
+Q10770
@@ Property / Symbols used: Q10770 / rank @@
+Normal rank
@@ Property / Symbols used: Q10770 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ 
\diff{\NVar{x}}
@@ Property / Symbols used: Q10770 / qualifier @@
+xml-id: C1.S4.SS4.m1adec
@@ Property / Symbols used @@
+Q10771
@@ Property / Symbols used: Q10771 / rank @@
+Normal rank
@@ Property / Symbols used: Q10771 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\int}}$ 
\int
@@ Property / Symbols used: Q10771 / qualifier @@
+xml-id: C1.S4.SS4.m3adec
@@ Property / Symbols used @@
+Q11447
@@ Property / Symbols used: Q11447 / rank @@
+Normal rank
@@ Property / Symbols used: Q11447 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}$ 
\assLegendreP[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreP[0]{\nu}@{z}
@@ Property / Symbols used: Q11447 / qualifier @@
+xml-id: C14.S2.SS2.p2.m3aadec
@@ Property / Symbols used @@
+Q11589
@@ Property / Symbols used: Q11589 / rank @@
+Normal rank
@@ Property / Symbols used: Q11589 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q11589 / qualifier @@
+xml-id: C14.S1.XMD1.m1edec
@@ Property / Symbols used @@
+Q11593
@@ Property / Symbols used: Q11593 / rank @@
+Normal rank
@@ Property / Symbols used: Q11593 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle m}}$ 
m
@@ Property / Symbols used: Q11593 / qualifier @@
+xml-id: C14.S1.XMD5.m1edec
@@ Property / Symbols used @@
+Q11590
@@ Property / Symbols used: Q11590 / rank @@
+Normal rank
@@ Property / Symbols used: Q11590 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q11590 / qualifier @@
+xml-id: C14.S1.XMD8.m1edec

DLMF:14.6.E6 (Q4748): Difference between revisions

𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

∫ {\displaystyle{\displaystyle\int}}

P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}

x 𝑥 {\displaystyle{\displaystyle x}}

m 𝑚 {\displaystyle{\displaystyle m}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

Latest revision as of 01:27, 2 January 2020

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${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}$

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

${\displaystyle{\displaystyle\int}}$

${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}$

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle m}}$

${\displaystyle{\displaystyle\nu}}$